Question - Finding the Equation of a Line with a Given Slope and Point
Solution:
$$\text{Given slope (m)} = 2, \text{ and point } (x_1, y_1) = (1, 3)$$$$\text{Use point-slope form: } y - y_1 = m(x - x_1)$$$$y - 3 = 2(x - 1)$$$$y - 3 = 2x - 2$$$$y = 2x + 1$$
Tutor Solution:
To find the equation of a line with a given slope that passes through a specific point, we can use the point-slope formula:\[ y - y_1 = m(x - x_1) \]where $$ m $$ is the slope, and $$ (x_1, y_1) $$ is the point the line passes through.Given the slope $$ m = 2 $$ and the point $$ (1, 3) $$, we plug these values into the point-slope formula:\[ y - 3 = 2(x - 1) \]Now, we will distribute the 2 on the right side of the equation to get:\[ y - 3 = 2x - 2 \]Next, to get the equation in the slope-intercept form $$ y = mx + b $$, we will add 3 to both sides of the equation:\[ y = 2x - 2 + 3 \]Finally, combine like terms to obtain the standard slope-intercept form:\[ y = 2x + 1 \]So the equation of the line with a slope of 2 passing through the point (1, 3) is $$ y = 2x + 1 $$.
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